Explain the determine yellow and the inf is here The objective of this article is to investigate somequalitative behavior of the solutions of the nonlineardifference equationbxn-k[dxp=k– eXp–1]Xn+1 =Axn+ Bxn-k+ Cxp–1+Dxp-n= 0,1,2, ....(1)where the coefficients A, B, C, D, b, d, e E (0, 0), whilek, 1 and o are positive integers. The initial conditionsi,.……, X_1,..., X_ky •……, X_1, Xo are arbitrary positive realnumbers such that k < 1< 0. Note that the special casesof Eq.(1) have been studied in [1] when B= C = D= 0,and k = 0,1= 1, b is replaced by – b and in [27] whenB=C= D=0, and k= 0, b is replaced by[33] when B = C = D = 0, 1= 0 and in [32] whenA= C=D=0, 1=0, b is replaced by – b.b and in| Theorem 9.If k is even and 1, 0 are odd positive integers,then Eq.(1) has prime period two solution if the conditiont(1–(C+D)) (3e– d) < (e+ d) (A+ B),(20)isvalid,provided(C+D)1ande (1– (C+ D)) – d (A+B) > 0.aProof.If k is even and 1, o are odd positive integers, thenXn = Xn-k and xn+1 = Xn-1= Xn-o• It follows from Eq.(1)thatbQP= (A+B) Q+(C+D)P –(21)(еР — dQ)"andVБРQ= (A+B) P+(C+D) Q –(22)(eQ– dP)'Consequently, we gete P – dPQ = e (A+B) PQ– d (A+B) Q + e(C+ D) P- (C+D) dPQ– bQ,(23)ande Q – dPQ = e (A+B) PQ– d (A+B) +e(C+D) Q- (C+D) dPQ– bP.i%3D(24)By subtracting (24) from (23), we getP+Q=(25)[e (1– (C+D))– d (A+B)]’where e (1-(C+ D)) – d (A+B) > 0. By adding (23)and (24), we obtainte b (1 – (C+D))(e+d) [K1+(A+B)][e K1 – d (A+B)]² 'PQ=(26)(1–(C+D)), provided (C+D) < 1.where K1 =Assume that P and Q are two positive distinct real rootsof the quadratic equation2- (P+Q)t+ PQ=0.(27)Thus, we deduce that(P+ Q)² > 4PQ.(28)Substituting (25) and (26) into (28), we get the condition(20). Thus, the proof is now completed.O

Name: Explain the determine yellow and the inf is here The objective of this
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Description: Explain the determine yellow and the inf is here The objective of this article is to investigate somequalitative behavior of the solutions of the nonlineardifference equationbxn-k[dxp=k– eXp–1]Xn+1 =Axn+ Bxn-k+ Cxp–1+Dxp-n= 0,1,2, ....(1)where the co